Question: Simplify to lowest terms. $\dfrac{50}{20}$
Explanation: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 50 and 20? $50 = 2\cdot5\cdot5$ $20 = 2\cdot2\cdot5$ $\mbox{GCD}(50, 20) = 2\cdot5 = 10$ $\dfrac{50}{20} = \dfrac{5 \cdot 10}{ 2\cdot 10}$ $\hphantom{\dfrac{50}{20}} = \dfrac{5}{2} \cdot \dfrac{10}{10}$ $\hphantom{\dfrac{50}{20}} = \dfrac{5}{2} \cdot 1$ $\hphantom{\dfrac{50}{20}} = \dfrac{5}{2}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{50}{20}= \dfrac{2\cdot25}{2\cdot10}= \dfrac{2\cdot 5\cdot5}{2\cdot 5\cdot2}= \dfrac{5}{2}$